成层半空间出平面自由波场的一维化时域算法

提出了一种计算出平面SH波斜入射时弹性水平成层半空间中自由波场时域计算的一维化有 限元方法. 在进行有限元网格划分时,竖向单元取满足有限元模拟精度的任意尺寸,水平向 网格尺寸由时间离散步长和水平视波速确定,并自动进行虚拟网格划分. 基底设置人工边界, 并将波动输入转化为等效荷载施加在边界节点上. 然后将集中质量有限元法和中心差分法相 结合建立节点运动方程,并将水平方向相邻节点的运动用该节点相邻时刻的运动表示,从而 将求解节点运动的二维方程组转化为一维方程组. 求解此方程组,即得到自由场中竖向一列 节点的运动. 最后根据行波传播的特点,可方便地确定全部自由波场. 理论分析和数值算例 表明,该方法具有较高的精度和良好的稳定性.     

弹性半空间二维出平面自由波场的一维化时域算法

提出了一种计算出平面SH波斜入射时弹性半空间自由波场时域计算的一维化有限元方法。首先利用Snell定律确定平面波沿水平方向的传播规律,在用有限元法对弹性半空间进行离散化时,竖向单元尺寸根据波动有限元模拟精度要求确定,而水平向有限元网格尺寸根据水平向波的传播规律和采用的离散时间步长确定,使得有限元离散模型中任意节点的运动可以用水平向相邻节点的运动表示,从而将二维有限元节点运动方程组化为一维的形式。求解此一维方程组,可得到弹性半空间中一列节点的运动,再根据行波的传播规律,可确定全空间自由波场。理论分析和数值算例表明,该方法具有较高的精度和良好的稳定性。     

A new method for the generation of representative time-domain turbulence excitations

In this paper we address the issue of generating, from the spectral and spatial parameters of turbulent flow excitations, time-domain random excitations suitable for performing representative nonlinear numerical simulations of the dynamical responses of flow-excited tubes with multiple clearance supports. The new method proposed in this work, which is anchored in a sound physical basis, can effectively deal with non-uniform turbulent flows, which display significant changes in their spatial excitation properties. Contrary to the classic technique developed by Shinozuka and coworkers, which generates a large set of correlated physical forces, the proposed method directly generates a set of correlated modal forces. Our approach is particularly effective leading to a much smaller number of generated time-histories than would be needed using physical forces to simulate the turbulence random field. In the case of strongly non-uniform flows, our approach allows for a suitable decomposition of the flow velocity profile, so that the spectral properties of the turbulence excitation are modeled in a consistent manner. The proposed method for simulating turbulence excitations is faster than Shinozuka׳s technique by two orders of magnitude. Also, in the framework of our modal computational approach, nonlinear computations are faster, because no modal projection of physical turbulent forces is needed. After presenting the theoretical background and the details of the proposed simulation method, we illustrate it with representative linear and nonlinear computations performed on a multi-supported tube.     

A novel type of transverse surface wave propagating in a layered structure consisting of a piezoelectric layer attached to an elastic half-space

The existence and propagation of transverse surface waves in piezoelectric coupled solids is investigated, in which perfect bonding between a metal/dielectric substrate and a piezoelectric layer of finite-thickness is assumed. Dis- persion equations relating phase velocity to material con- stants for the existence of various modes are obtained in a simple mathematical form for a piezoelectric material of class 6mm. It is discovered and proved by numerical examples in this paper that a novel Bleustein-Gulyaev （B-G） type of transverse surface wave can exist in such piezoelectric cou- pled solid media when the bulk-shear-wave velocity in the substrate is less than that in the piezoelectric layer but greater than the corresponding B-G wave velocity in the same pie- zoelectric material with an electroded surface. Such a wave does not exist in such layered structures in the absence of pie- zoelectricity. The mode shapes for displacement and electric potential in the piezoelectric layer are obtained and discussed theoretically. The study extends the regime of transverse sur- face waves and may lead to potential applications to surface acoustic wave devices.     

A note on the diffraction of an obliquely incident surface wave by a partially immersed fixed vertical barrier

The problem of the diffraction of surface waves, obliquely incident on a partially immersed fixed vertical barrier in deep water, is solved approximately by reducing it to the solution of an integral equation, for small angle of incidence of the incident wave. The corrections to the reflection and transmission coefficients over their normal incidence values for small angle of incidence are obtained and presented graphically for some intermediate values of wave numbers.     

A dynamic problem for a prestressed compressible layered half-space

The linearized theory of elasticity for prestressed bodies is used to solve a stationary plane problem for a prestressed two-layer half-space under a surface load moving with constant velocity. The half-space is assumed to be compressible and to have an arbitrary elastic potential. The Fourier transform is used to obtain the fundamental solution of the problem for different contact conditions and load velocities. A compressible material with a harmonic elastic potential is considered as an example __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 35–55, April 2008.     

Surface effect on Bleustein-Gulyaev wave in a piezoelectric half-space

Surface effect, which is attributed to the different environment surrounding the surface or near-surface atoms from that embracing the bulk atoms, may become significant when the surface-to-volume ratio of a body is large. This paper considers the effect of a plane boundary of a piezoelectric body modeled as a thin layer with specified material properties, for which a transfer relation between the state vectors at the top and bottom surfaces is derived based on the state-space formulations. The equations of surface piezoelectricity for different orders without any bias field are then presented by making use of the power series expression of the transfer matrix. The surface effect is demonstrated by considering the Bleustein-Gulyaev wave existing in a horizontally polarized piezoceramic half-space.     

Axisymmetric wave propagation in a layered transversely isotropic medium

Summary In this paper, the method of numerical integration along bicharacteristics is generalized to the case of layered transversely isotropic medium for analysing the axisymmetric stress wave propagation. The stability of the present scheme is studied. The advantages and limitations of the method are discussed. Received 12 June 1996; accepted for publication 6 May 1997     

GENERALIZED FINITE SPECTRAL METHOD FOR 1D BURGERS AND KDV EQUATIONS

A generalized finite spectral method is proposed. The method is of high-order accuracy. To attain high accuracy in time discretization, the fourth-order Adams-Bashforth-Moulton predictor and corrector scheme was used. To avoid numerical oscillations caused by the dispersion term in the KdV equation, two numerical techniques were introduced to improve the numerical stability. The Legendre, Chebyshev and Her-mite polynomials were used as the basis functions. The proposed numerical scheme is validated by applications to the Burgers equation (nonlinear convection- diffusion problem) and KdV equation (single solitary and 2-solitary wave problems), where analytical solutions are available for comparison. Numerical results agree very well with the corresponding analytical solutions in all cases.     

Localization of wave motions in a fluid-filled cylinder

The properties of harmonic surface waves in a fluid-filled cylinder made of a compliant material are studied. The wave motions are described by a complete system of dynamic equations of elasticity and the equation of motion of a perfect compressible fluid. An asymptotic analysis of the dispersion equation for large wave numbers and a qualitative analysis of the dispersion spectrum show that there are two surface waves in this waveguide system. The first normal wave forms a Stoneley wave on the inside surface with increase in the wave number. The second normal wave forms a Rayleigh wave on the outside surface. The phase velocities of all the other waves tend to the velocity of the shear wave in the cylinder material. The dispersion, kinematic, and energy characteristics of surface waves are analyzed. It is established how the wave localization processes differ in hard and compliant materials of the cylinder __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 72–86, April 2008.     

The semi-discrete method for solving high-dimension wave equation

The article gives a semi-discrete method for solving high-dimension wave equation. By the method, high-dimension wave equation is converted by means of discretization into I-D wave equation system which is well-posed. The convergence of the semidiscrete method is given. The numerical calculating results show that the speed of convergence is high.     

A new auxiliary equation method for finding travelling wave solutions to KdV equation

In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the （1＋1）-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which cover the existing solutions. Compared to other methods, the presented method is more direct, more concise, more effective, and easier for calculations. In addition, it can be used to solve other nonlinear evolution equations in mathematical physics.     

A 1D Roe decomposition of a system of equations governing wave height transformation

A Roe‐type decomposition for a system of equations governing onshore/offshore wave transformation in coastal waters is derived. The equation set approximated pertains to coastal waters prior to wave breaking, and is based on depth‐averaging and time‐averaging of the Euler equations. The equations are those used in many commercial codes for simulation of wave height and wave‐averaged currents. This novel approach uses a combination of some standard Roe averages, together with physical reasoning and power series expansions to derive a Roe‐averaged Jacobian (with real, linearly independent eigenvectors) and ensures conservation, and thereby effects the decomposition. It is shown that the resulting derived Roe‐averaged quantities are accurate to a high degree, by comparing them with their analytical equivalents for a wide range of nondimensional water depths and slopes likely to be encountered in coastal problems. Numerical tests of time‐invariant wave height transformation and wave group propagation are undertaken; these indicate good performance of the scheme in practice. Copyright © 2011 John Wiley & Sons, Ltd.     

一种求解瑞利波散射问题的修正边界元方法

边界元法的一大优势是用于求解半空间等无限域问题,但在求解弹性波的传播问题中,传统边界元法采用的全平面或全空间格林函数会在截断边界处产生虚假的反射回波,这会引起散射场求解的误差.为了避免这种误差,论文在传统边界元法基础上提出一种修正边界元法,该修正方法主要包括:以瑞利波形式的远端散射场代替原本因截断而舍去的部分,通过互易定理建立单位瑞利波和全平面格林函数的积分方程,求得修正系数,并代入修正边界元矩阵,计算出瑞利波的散射场.文中基于该方法计算了无缺陷平面的瑞利波(与解析解的误差为1.24×10-5),并运用该方法计算了不同缺陷的散射场.由文中对比结果表明,论文所提修正边界元法可准确求解瑞利波散射场,为基于表面波的缺陷反演问题研究提供了有效的正演途径.     

A new fully non‐hydrostatic 3D free surface flow model for water wave motions

A new fully non‐hydrostatic model is presented by simulating three‐dimensional free surface flow on a vertical boundary‐fitted coordinate system. A projection method, known as pressure correction technique, is employed to solve the incompressible Euler equations. A new grid arrangement is proposed under a horizontal Cartesian grid framework and vertical boundary‐fitted coordinate system. The resulting model is relatively simple. Moreover, the discretized Poisson equation for pressure correction is symmetric and positive definite, and thus it can be solved effectively by the preconditioned conjugate gradient method. Several test cases of surface wave motion are used to demonstrate the capabilities and numerical stability of the model. Comparisons between numerical results and analytical or experimental data are presented. It is shown that the proposed model could accurately and effectively resolve the motion of short waves with only two layers, where wave shoaling, nonlinearity, dispersion, refraction, and diffraction phenomena occur. Copyright © 2010 John Wiley & Sons, Ltd.     

固体中短波传播单位分解有限元法的解析积分

针对固体中短波传播数值模拟的单位分解有限元法中单元矩阵积分的被积函数的强烈振荡特性,应用直角坐标系下标准有限元形函数和单元内的波动方向知识提出了一种单元矩阵的解析积分方案。它对于平面三,六,四,八和九节点的直边单位分解有限单元是完全解析的,对于与这些单元相应的曲边单元则是半解析的。数值结果显示所提出的积分方案在计算效率上比高斯-勒让德积分有大幅度提高。     

用改进的ghost fluid方法模拟强激波与界面的相互作用

为了解决原来的ghost fluid方法在计算强激波和界面相互作用时界面附近出现的速度和压力振荡问题,对原来的ghost fluid方法进行了改进,通过在界面处构造Riemann问题并求出界面的压力和速度,ghost fluid流体的压力和速度分别用界面的压力和速度代替,ghost流体的密度通过熵常数外推得到。改进的ghost fluid保持了原来的ghost fluid的简单性,对一维强激波与气-气、气-液界面的相互作用问题以及射流问题进行了数值计算,得到了分辨率较高的计算结果。     

An interpolated time-domain equivalent source method for modeling transient acoustic radiation over a mass-like plane based on the transient half-space Green’s function

Interpolated time-domain equivalent source method (ITDESM) is based on the assumption of free space, which makes it not suitable for reconstructing the transient acoustic quantities in the half space. Here, a half-space ITDESM is proposed to model the transient acoustic radiation over a mass-like plane. In this method, the free transient Green’s function existing in the conventional ITDESM is replaced by a closed-form transient half-space Green’s function for a mass-like plane. Such transient Green’s function enables one to take the reflection effect of the mass-like plane into consideration. Modeling acoustic radiation from three transient monopoles above an infinite plane with mass-like behavior is studied by numerical simulations to demonstrate the feasibility of the half-space ITDESM. The proposed method is also examined by comparing the reconstruction accuracy among a free-field model, a rigid plane model and a mass-like plane model. An experiment with an impacted steel plate lying above a table plate is conducted in the semi-anechoic room, and the results further verify the effectiveness of the proposed method.     

一种非对称大型有限元方程组的有效分块波前解法

提出分块波前法求解非对称大型有限元方程组，该方法综合分块解法和波前法的优点，根据计算机容量和方程的阶数优化计算过程，以在经济效率和存储效率之间达到平衡。本文利用该方法求解了轮胎稳态滚动有限元方程组，表明该方法是有效、可靠的。     

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

In this work, the three-dimensional(3 D) propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP) and quasi-shear(qS1 and qS2) modes are derived. Based on the transfer and stiffness matrices, band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap prope...